NB Grade 5 Math common mistakes
NB Grade 5 Math · Understand the traps and how to avoid them.
When reading or writing a large whole number, the student drops or misplaces a zero in the middle of a number (writing 4,063 as 463 or 4,603), changing its value by thousands.
The student treats zeros as empty placeholders that can be skipped rather than as digits that hold a place open, and does not systematically chunk the number into groups of three from the right before writing it.
What to do instead
Have the student build the number with place-value materials or a place-value chart, saying each place aloud ('4 thousands, 0 hundreds, 6 tens, 3 ones'), then write it. Practise chunking: mark groups of three digits from the right, read each group with its unit name, and check that every place in the chart has a digit, including zeros.
The student adds or subtracts fractions with unlike denominators by adding both numerators and denominators (1/2 + 1/3 = 2/5) or by adding numerators while keeping one of the denominators unchanged.
The student generalises whole-number addition rules to fractions and has no mental image of the sum, so the answer 2/5 (less than 1/2) is never checked against the reasonable size of the result.
What to do instead
Use fraction strips or number lines to show that halves and thirds are different-sized pieces and cannot be counted together until the pieces match. Have the student rename each fraction to a common denominator using equivalent-fraction reasoning, then estimate the answer first (about 1) and compare it with the computed result.
The student compares decimals such as 0.7 and 0.65 by counting digits or by treating the decimal as two whole numbers, concluding 0.65 is larger because 65 is larger than 7.
The student reads the digits after the decimal point as a whole number rather than as tenths and hundredths, and lacks a length or money model that would make the order visible.
What to do instead
Have the student model both numbers with base-ten blocks or on a number line and rename them with the same denominator (0.70 and 0.65). Use a money context (70 cents versus 65 cents) and line up place values vertically, filling empty places with zeros before comparing digit by digit from the left.
The student continues a growing or shrinking pattern by copying the differences between consecutive terms instead of applying the rule, so a pattern that adds 3 then 5 then 7 is extended by repeatedly adding 7.
The student looks only at the last two terms rather than testing a rule against all terms, and has not distinguished between a constant difference and a changing difference.
What to do instead
Have the student make a table of terms and differences, test a proposed rule against every pair of terms in the table, and state the rule in words before predicting the next term. Include patterns with changing differences and patterns that multiply, so the student checks the whole sequence rather than one step.
Given a description of a relationship, the student writes an expression or equation with the operations reversed, writing 3n + 5 when the rule is 'multiply the number by 5 and add 3'.
The student translates the words in order without identifying which quantity is the input and which operation acts on it, and does not verify the rule with a test value.
What to do instead
Have the student build a table of input-output pairs from the description, then test each candidate expression on at least two inputs. Encourage the student to read the sentence in chunks ('start with the number', 'multiply by 5', 'then add 3') and write one step per line before combining into a single expression.
When finding the area or perimeter of a rectangle, the student uses the wrong formula, adding the sides for area or multiplying for perimeter, or mixes units such as cm and m in the same calculation.
The student memorises the formulas as strings of symbols without connecting them to the meaning of covering a surface versus going around the edge, and does not convert units before computing.
What to do instead
Have the student cover the rectangle with unit squares to see area as the number of squares and trace the boundary with a finger or string to see perimeter as a length. Label every measurement with its unit, convert all measurements to the same unit before calculating, and record the answer with square units for area and linear units for perimeter.
The student calculates the mean of a data set by adding the values and dividing by the number of different values or by the largest value, rather than by the number of data points, or reports the median when the mean is requested.
The student confuses the three measures of centre and does not connect the mean to the idea of sharing the total equally among all the data points.
What to do instead
Have the student use a concrete 'levelling' model: stack counters for each value and redistribute them so all stacks are equal, then record the total and the number of stacks. For each data set, ask the student to name which measure is requested, compute all three, and explain in words what each one represents.
The student predicts the outcome of a simple probability experiment by assuming the most recent results determine the next one, saying a tail is 'due' after several heads, or judges likelihood from personal preference rather than from the possible outcomes.
The student applies a 'fairness' intuition that past results must balance out in the short run, and has limited experience recording outcomes to see how variability and long-run frequency behave.
What to do instead
Have the student list all possible outcomes for a spinner or bag of counters, then run the experiment many times and record results in a tally or table. Compare the experimental results with the predicted likelihoods and discuss why small samples vary while larger samples tend to approach the predicted pattern.
After solving a word problem, the student gives a numerical answer with no unit, no label, or a value that is impossible in context (such as 12.5 buses) and does not check it against the question.
The student treats problem solving as extracting numbers and applying an operation, skipping the steps of identifying what is asked and interpreting the result in the situation.
What to do instead
Require a written plan before computing: restate the question in the student's own words, list the given information with units, choose an operation and justify it, then compute and write a full sentence answer with units. Finish by asking whether the answer makes sense in the story and rounding where the context requires a whole number.
The student solves a multi-step problem by performing only the first operation and stopping, or by using every number in the problem regardless of whether it is needed.
The student reads the problem once and begins computing immediately, without breaking the problem into parts or identifying which information is relevant and which is extra.
What to do instead
Teach a routine: read the problem twice, underline the question, cross out unneeded information, and write a numbered list of the steps needed before calculating. Have the student explain each step in words and check the final answer against the original question, then solve a parallel problem with one piece of information changed.